tenoch

food_energy.tex

@@ -29,7 +29,7 @@ Science and Social Policy classes are full of bespoke units and involve many dif
 \maketitle
 
 \section{Introduction}
-When the United States entered World War One one of the problems they faced was logistics.  How much food do you need to ship overseas to Europe to feed a million soldiers?  That early work in nutrition led to the 3000 Calorie diet many people remember from secondary Health Education class.  A bit about units you might remeber: $1~Calorie = 1~kilocalorie~(kcal)$, and a dietician might build a $3000 kcal$ diet for a 20 year old basketball player.  A \textit{calorie} is the amount of energy it takes  to heat a gram of water by a degree Celsius.  There are about 4.2 Joules in a single calorie, and a Joule occurs all over introductory  physics.  If you need to buy a new home furnace, the sales brochure might advertise that it is capable of delivering 100,000 BTU's of heat each hour.  What's a BTU? Heat a pound of water by $1^{\circ}F$.  Of course Heat Pumps are far more efficient than simply burning methane or propane, but they consume kilo-watt-hours (kWh) of electricity, not BTU's.  What's a kWh?  Run a 1000 Watt toaster for an hour and you'll have pulled one kWh off the grid, it will cost you about \$0.13 in Minnesota.  If you decide to put solar panels in your backyard, they will probably collect about $10\%$ of the 3.5kWh the  the sun delivers to each square meter of your lawn (in Minnesota) each day.  
+When the United States entered World War One one of the problems they faced was logistics.  How much food do you need to ship overseas to Europe to feed a million soldiers?  That early work in nutrition led to the 3000 Calorie diet many people remember from secondary Health Education class.  A bit about ``Calorie'' (uppercase) vs ``calorie'' (lowercase) units you might remeber: $1~Calorie = 1~kilocalorie~(kcal)$, and a dietician might build a $3000 kcal$ diet for a 20 year old basketball player.  A \textit{calorie} is the amount of energy it takes  to heat a gram of water by a degree Celsius.  There are about 4.2 Joules in a single calorie, and a Joule occurs all over introductory  physics.  If you need to buy a new home furnace, the sales brochure might advertise that it is capable of delivering 100,000 BTU's of heat each hour.  What's a BTU? Heat a pound of water by $1^{\circ}F$.  Of course Heat Pumps are far more efficient than simply burning methane or propane, but they consume kilo-watt-hours (kWh) of electricity, not BTU's.  What's a kWh?  Run a 1000 Watt toaster for an hour and you'll have pulled one kWh off the grid, it will cost you about \$0.13 in Minnesota.  If you decide to put solar panels in your backyard, they will probably collect about $10\%$ of the 3.5kWh the  the sun delivers to each square meter of your lawn (in Minnesota) each day.  
 
 As the previous paragraph illustrates, there are a frustratingly large number of different units in an ``Energy'' class.  At Winona State, this 3 credit class fulfulls a ``Science and Social Policy'' general education requirement and is taken by students from across the university.   Lots of college majors don't require a math class beyond algebra or introductory statistics and the population is largely math-averse. You could jokingly say that one of the main things students learn in the class is unit converstion, but it isn't far off.  Nearly every field finds energy a useful representation, and every profession has their own set of units and terminology that's most well suited for quick calculation.  Would a medical lab scientist talk about the fractional acre-foot of urine needed test kidney function?  No, but someone in the central valley of California would certianly care about the acre-feet of water necessary to grow almonds!  Does a gas station price their gasoline in dollars per kWh? Given the growing electrification of cars, they might soon.
 
@@ -39,8 +39,17 @@ Everyone eats, maybe not $3000 kcals$ per day, but at least something every day.
 
 To introduce Food Energy, I ask the students to work through a few questions:
 
+\begin{figure}[h]
+\centering
+\includegraphics[width=\columnwidth]{at_the_buffet.jpg}
+\caption{
+A proto-college-student at Winona's China King Buffet, dreaming about visiting the steam tables every day. 
+}
+\label{buffet}
+\end{figure}
+
 \subsection{Converting food into body heat}
-Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am.  If he brings homework and stretches the meal out for a few hours he can get all $3000~kcals$ with only one meal bill.  Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get? 
+Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am, eg figure \ref{buffet}.  If he brings homework and stretches the meal out for a few hours he can get all $3000~kcals$ with only one meal bill.  Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get? 
 Useful information: the student has a mass of 80kg and is made mostly of water.  A Calorie heats 1 kg of water $1^{\circ}C$. 
 
 Here's a possible answer:
@@ -49,7 +58,7 @@ equate food energy with calorimetric heating and assume human bodies have the sa
 3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T\\
 \Delta T &\approx& +37.5\degC
 \eea
-Students are normally quite surprised at this number.  Although wildly unrealistic, $\Delta T \approx +6\degC$ is typicaly fatal, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this calculation to feeling quite hungry after a cold swim in the pool (a similar effect).  On a larger scale, discussing what's wrong with this estimate is useful.  The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores.  Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby growing enough fat tissue to store sufficient kcals to make it though a night without waking up ravenously hungry.  A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout}  The contrast of bear hibernation \cite{fat_bear} and songbirds constatly eating through the winter are related connections to investigate.
+Students are normally quite surprised at this number.  Although wildly unrealistic, $\Delta T \approx +6\degC$ is typicaly fatal, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this calculation to feeling quite hungry after a cold swim in the pool (a similar effect).  On a larger scale, discussing what's wrong with this estimate is useful.  The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores.  Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby developing enough fat tissue to store sufficient kcals to make it though a night without waking up ravenously hungry.  A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout}  The contrast of bear hibernation \cite{fat_bear} and songbirds constantly eating through the winter are related connections to investigate.
 
 \subsection{Biophysical Power}
 A more realistic question to follow up with relates to the average \textit{power} given off by a person over a day.  
@@ -59,7 +68,7 @@ Again, assuming $3000kcal$ is burned over $24 hours$, with useful information: $
 \ee
 Most students still remember $75Watt$ lightbulbs, but given the spread of LED lighting, ``A person's body heat is two 75W light bulbs'' will probably only make sense for a few more years.  Desert or cold-weather camping, alone versus with friends, and survival swimming are also examples for students to make sense of this answer.  If you can take advantage of other people's waste body heat, you'll sleep more pleasantly and survive longer in cold water.  
 
-Another application to discuss is that of ``brown fat,'' a sort of biological space heater that humans and other mammals develop in response to cold weather.  This tissue's mitochondria can burn lipids and carbohydrates in a useless proton pumping scheme, which produces metabolic heat \cite{brown_fat}.  Most common in rodents and infants, this mechanism can be stimulated by extended exposure to cold temperatures.  The idea of a biological space heater that takes a month to turn on and a month to turn off matches the lived experience of college students in Minnesota, who wear down jackets in $4\degC$ weather in November, and beachwear in the same $4\degC$ weather in March.  Additionally, transplants to northern climates often take a few years to ``get used to'' the colder weather up north. It seams just as easy to say that transplants' bodies take a few years to develop the brown fat cells which allow them to be comfortable in cold weather.
+Another application to discuss is that of ``brown fat,'' a sort of biological space heater that humans and other mammals develop in response to cold weather.  This tissue's mitochondria can burn lipids and carbohydrates in a useless proton pumping scheme, which produces metabolic heat \cite{brown_fat_1,brown_fat_2,brown_fat_3,brown_fat_4}.  Most common in rodents and infants, this mechanism can be stimulated by extended exposure to cold temperatures -- the original work was done on lumberjacks in Finland \cite{finland_lumberjacks} .  The idea of a biological space heater that takes a month to turn on and a month to turn off matches the lived experience of college students in Minnesota, who wear down jackets in $4\degC$ weather in November, and beachwear in the same $4\degC$ weather in March.  Additionally, transplants to northern climates often take a few years to ``get used to'' the colder weather up north. It seems just as easy to say that transplants' bodies take a few years to develop the brown fat cells which allow them to be comfortable in cold weather.
 
 One other distinction to emphasize is the difference between power and energy.  A graph of a human body's ``kcal content'' over the course of a day can be a useful illustration.  When sedentary, this graph probably has the slope of $-150W\approx -125 \frac{kcals}{hour}$.  If the $3000kcal$ meal at the buffet takes an hour, this period corresponds to an energy-time slope of $+3000\frac{kcal}{hour}\approx +3500W$.  
 
@@ -91,7 +100,7 @@ This estimate is again surprising to students.  Five trips up the bluff to burn
 The point of these energy calculations is not to give students an eating disorder.  Rather, the numbers show food's amazing power. A single slice of toast will bring a car up to the residential speed limit!  A day's food, $3000kcal$, will power you up an $8000m$ mountain peak! The body-work food allows us to do is astonishing, and increases in food production have made modern  comforts, unimaginable 150 years ago, possible to the point of being taken for granted.  
 
 \subsection{Where does food energy come from?}
-One feature of the aught's ``homesteading'' culture \cite{homesteading} is the idea that a person should probably be able to move to the country, eat a lot of peaches, and grow all their own food.  Learning that farming labor is \textit{skilled} labor can be a brutal and disheartening realization. Eating $3000kcals$ each day means planting, weeding, harvesting, and storing more than a million kcals each year \cite{Haspel}.  Where will those Calories come from? Is your backyard enough to homestead in the suburbs \cite{backyard_homestead}?
+One feature of the aught's ``homesteading'' culture \cite{homesteading} is the idea that a person should probably be able to move to the country, eat a lot of peaches, and grow all their own food.  Learning that farming labor is \textit{skilled} labor can be brutal and disheartening. Eating $3000kcals$ each day means planting, weeding, harvesting, and storing more than a million kcals each year \cite{Haspel}.  Where will those Calories come from? Is your backyard enough to homestead in the suburbs \cite{backyard_homestead}?
 
 At some point bewteen 1920 and 1950, US chemical manufacturers realized that in the post-war period, they could repurpose processes developed for manufacturing munitions and chemical warfare agents, to produce chemicals that would kill insects and increase the nitrogen levels in the soil. 
 As figures \ref{corn_and_potato_yields} and \ref{ag_yields} show, the epoch of ``Better Living Through Chemistry'' produced a dramatic increase in per-acre yields across all comodity food crops, particularly corn and potatoes.  
@@ -133,7 +142,7 @@ A table from a USDA booklet giving 1917 yields for various farm products.
 \end{figure}
 
 So, another question using this data.  If you want to feed your family of four people potatoes, how much land will you need to cultivate?
-Here's an estimate: a family of 4 requires 3000kcal/person each day.  If we over-estimate and produce food for the entire year, the family will need about $4.4$ million kcals.
+Here's an estimate: a family of 4 requires 3000kcal/person each day\cite{calorie_age}.  If we over-estimate and produce food for the entire year, the family will need about $4.4$ million kcals.
 \be
 4~people\cdot\frac{3000kcal}{person\cdot day}\cdot\frac{365~days}{year} \approx 4.4 M kcal 
 \ee
@@ -164,11 +173,16 @@ More emotionally charged conversations can be had about converting the United St
 % 113M acres / 5.1 ~= 22M acres
 
 \section{Example: How big could Tenochtitlan have been?}
-The questions described thus far have largely been centered within a physics context.  The paper closes with two more examples that leverage this food energy picture to make historical claims.  The first example relates to the pre-columbian capital of the Aztec Empire, Tenochtitlan, now known as Mexico City.  Tenochtitlan was build on and around a endorheic lake, Texcoco.  Crops were grown in shallow parts of the lake via chinampas \cite{national_geo}, floating patches of decaying vegetation and soil.  Given the proximity to water and decaying vegetation, these fields were very fertile and productive and some continue to be used in the present day \cite{google_earth}.  
+The questions described thus far have largely been centered within a physics context.  The paper closes with two more examples that leverage this food energy picture to make historical claims.  The first example relates to the pre-columbian capital of the Aztec Empire, Tenochtitlan, now known as Mexico City.  Tenochtitlan was build on and around a endorheic lake, Texcoco.  Crops were grown in shallow parts of the lake via chinampas \cite{national_geo}, floating patches of decaying vegetation and soil.  Given the proximity to water and decaying vegetation, these fields were very fertile \cite{HortTech_2019,Chinampas_1964} and some continue to be used in the present day \cite{google_earth}.  
 
-Estimates of Tenochtitlan's population in 1500CE vary widely, from 40,000 \cite{40k} to more than 400,000 \cite{400k} inhabitants, comparable in size to Paris at that time. These estimates come both from oral and written records and estimates of archeological building density and land area.   While canibalism was part of Aztec religious ritual and practice \cite{Aztec_Cannibalism}, the staple Calorie sources for the Aztecs were corn and beans.
 
-Few if any Native American cultures made use of draft animals before the Columbian Exchange.  This means that the food that fed Tenochtitlan must have been brought to the city center by foot or canoe.  How much land must have been devoted to chinampas to feedg the population, or conversely, how many people could be supported by the land within walking or paddling distance from the city center?
+Estimates of Tenochtitlan's population in 1500CE vary widely, from 40,000 \cite{40k} to more than 400,000 \cite{400k} inhabitants, comparable in size to Paris at that time. These estimates come from oral and written records and estimates of archeological building density and land area.   While canibalism was part of Aztec religious ritual and practice \cite{Aztec_Cannibalism}, the staple Calorie sources for the Aztecs were corn and beans.
+
+Few if any Native American cultures made use of draft animals before the columbian exchange.  This means that the food that fed Tenochtitlan must have been brought to the city center by foot or canoe.  How much land must have been devoted to chinampas to feed the population, or conversely, how many people could be supported by the land within walking or paddling distance from the city center?
+
+look at map (wikipedia) of chinampas and compute area.  The ask what yield would produce sufficient corn - compare to 1917 data.  
+
+or, assume 40bu/acre, compute area, and find radius
 
 \section{Example: Was the Irish Potato Famine a Natural Disaster?}
 
@@ -194,14 +208,14 @@ John Deming, Carl Ferkinhoff, and Sarah Taber.
 The United States Department of Agriculture (USDA) provides historical crop information via the National Agricultureal Statistics Service, \url{https://www.nass.usda.gov/Statistics_by_Subject/index.php?sector=CROPS}.  Data was downloaded in spreadsheet csv format and then combined and plotted via a Python Jupyter notebook.   
 
 Each crop has its own bespoke units, for example potatoes are sold by hundredweight (CWT) but sugar beets are measured by the ton.  
-Every imaginable agricultural product seems to be tracked in the NASS site, for example Maple Syrup production is tracked and given in gallons of syrup per (tree) tap! 
+Every imaginable agricultural product seems to be tracked in the NASS site, for example Maple Syrup production is tracked and given in gallons of syrup per tap! 
 Conversion factors used are summarized in Table \ref{conversions}.  
 Calorie (kcal) density for each crop was taken from \url{https://fdc.nal.usda.gov/fdc-app.html}.  Within this database, foods are identified by an FDC ID.  
 
 An example calculation (implemented in the Jupyter notebook) follows for Corn.  
 In 2022 the USDA reported an average production of 172.3 bushels of corn per acre of farmland.  
 \be
-172.3\frac{bu}{acre}\cdot\frac{56lbs~corn}{bu}\cdot\frac{453.592~grams}{lbs}\cdot\frac{365~kcal}{100~grams} = 15,974,657 \frac{kcal}{acre}
+172.3\frac{bu}{acre}\cdot\frac{56lbs~corn}{bu}\cdot\frac{453.6~grams}{lbs}\cdot\frac{365~kcal}{100~grams} = 15,974,657 \frac{kcal}{acre}
 \label{example_calculation}
 \ee
 Obviously the result is only reasonable to two signifigant figures!
@@ -212,18 +226,21 @@ Obviously the result is only reasonable to two signifigant figures!
 
 \begin{table}
 \caption{\label{label}
-A summary of units and conversions used to create figure \ref{ag_yields} from USDA NASS data.  $1cwt$ is a hundred pounds of potatoes.  A bushel, $1bu$, is a volume unit of about 35liters and corresponds to about 60lbs of grain. Calorie content per 100 gram mass of food is taken from the USDA's ``Food Data Central'' database. It isn't clear from any of these resources if lb is pound-force (lbf) or pound-mass (lbm) and so I am ignorantly treating them as ``grocery store units'' where $1 lbs = 453.592 grams$.
+A summary of units and conversions used to create figure \ref{ag_yields} from USDA NASS data.  $1cwt$ is a hundred pounds of potatoes.  
+A bushel, $1bu$, is a volume unit of about 35liters and corresponds to about 60lbs of grain. Calorie content per 100 gram (mass) of food is taken from the USDA's ``Food Data Central'' database. 
+For context, typical serving sizes are included. 
+It isn't clear from any of these resources if lb is pound-force (lbf) or pound-mass (lbm) and so I am ignorantly treating them as ``grocery store units'' where $1 lbs \approx 453.6 grams$.
 }
 \begin{indented}
-\item[]\begin{tabular}{@{}lllll}
+\item[]\begin{tabular}{@{}llllll}
 \br
-Crop&per acre unit&production unit&kcals per 100gram &  FDC ID\\
+Crop&per acre unit&production unit&kcals per 100gram & typical portion &FDC ID\\
 \mr
-Corn & bu/acre & $1bu=56lbs$ & 365 &170288 \\
-Potatoes & cwt/acre & $1CWT=100lbs$ & 77 & 170026 \\
-Soybeans & bu/acre & $1bu=60lbs$ & 446 & 174270 \\
-Sunflowers & lbs/acre & & 584 & 170562 \\
-Wheat & bu/acre & $1bu=60lbs$ & 327 & 168890 \\
+Corn & bu/acre & $1bu=56lbs$ & 365 & 1 cup is 166g &170288 \\
+Potatoes & cwt/acre & $1CWT=100lbs$ & 77 & 0.5 cup is 75g & 170026 \\
+Soybeans & bu/acre & $1bu=60lbs$ & 446 & 1 cup is 186g &174270 \\
+Sunflowers & lbs/acre & & 584 & 1 cup is 140g & 170562 \\
+Wheat & bu/acre & $1bu=60lbs$ & 327 &  1 cup is 192g & 168890 \\
 \br
 \end{tabular}
 \end{indented}
@@ -263,23 +280,35 @@ The wilderness river might be full of trout, but if they're $300kcals$ each, you
 \bibitem{fat_bear}
 Some sources claim that bear metabolism can vary between $4,000$ to $20,000$ kcals per day, \url{https://bear.org/5-stages-of-activity-and-hibernation/}, comically illustrated by the National Park Service at \url{https://www.nps.gov/katm/learn/fat-bear-week-2022.htm} .
 
-\bibitem{brown_fat}
-Huttunen P, Hirvonen J, Kinnula V. The occurrence of brown adipose tissue in outdoor workers. Eur J Appl Physiol Occup Physiol. 1981;46(4):339-45. doi: 10.1007/BF00422121. PMID: 6266825.
 
+\bibitem{brown_fat_1}
 Brown and Beige Fat: Molecular Parts of a Thermogenic Machine
 Paul Cohen1 and Bruce M. Spiegelman2
 Diabetes 2015;64:2346–2351 | DOI: 10.2337/db15-0318
 
+\bibitem{brown_fat_2}
 https://pubmed.ncbi.nlm.nih.gov/33846638/
-Shamsi F, Piper M, Ho LL, Huang TL, Gupta A, Streets A, Lynes MD, Tseng YH. Vascular smooth muscle-derived Trpv1+ progenitors are a source of cold-induced thermogenic adipocytes. Nat Metab. 2021 Apr;3(4):485-495. doi: 10.1038/s42255-021-00373-z. Epub 2021 Apr 12. PMID: 33846638; PMCID: PMC8076094.
+Shamsi F, Piper M, Ho LL, Huang TL, Gupta A, Streets A, Lynes MD, Tseng YH. 
+Vascular smooth muscle-derived Trpv1+ progenitors are a source of cold-induced thermogenic adipocytes. Nat Metab. 2021 Apr;3(4):485-495. 
+doi: 10.1038/s42255-021-00373-z. Epub 2021 Apr 12. PMID: 33846638; PMCID: PMC8076094.
 
+\bibitem{brown_fat_3}
 https://pubmed.ncbi.nlm.nih.gov/14715917/
-Cannon B, Nedergaard J. Brown adipose tissue: function and physiological significance. Physiol Rev. 2004 Jan;84(1):277-359. doi: 10.1152/physrev.00015.2003. PMID: 14715917.
+Cannon B, Nedergaard J. Brown adipose tissue: function and physiological significance. Physiol Rev. 2004 Jan;84(1):277-359. 
+doi: 10.1152/physrev.00015.2003. PMID: 14715917.
 
+\bibitem{brown_fat_4}
 https://pubmed.ncbi.nlm.nih.gov/6722594/
-Himms-Hagen J. Nonshivering thermogenesis. Brain Res Bull. 1984 Feb;12(2):151-60. doi: 10.1016/0361-9230(84)90183-7. PMID: 6722594.
+Himms-Hagen J. Nonshivering thermogenesis. Brain Res Bull. 1984 Feb;12(2):151-60. 
+doi: 10.1016/0361-9230(84)90183-7. PMID: 6722594.
+%https://www.nih.gov/news-events/nih-research-matters/uncovering-origins-brown-fat
 
-https://www.nih.gov/news-events/nih-research-matters/uncovering-origins-brown-fat
+\bibitem{finland_lumberjacks}
+Huttunen P, Hirvonen J, Kinnula V. 
+The occurrence of brown adipose tissue in outdoor workers. 
+Eur J Appl Physiol Occup Physiol. 
+1981;46(4):339-45. 
+doi: 10.1007/BF00422121. PMID: 6266825.
 
 \bibitem{METS}
 Jetté M, Sidney K, Blümchen G. Metabolic equivalents (METS) in exercise testing, exercise prescription, and evaluation of functional capacity. Clin Cardiol. 1990 Aug;13(8):555-65. doi: 10.1002/clc.4960130809. PMID: 2204507.
@@ -293,22 +322,23 @@ Eric Brewe
 PHYSICAL REVIEW SPECIAL TOPICS - PHYSICS EDUCATION RESEARCH 7, 020106 (2011)
 https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.7.020106
 
-\bibitem{Haspel}
+\bibitem{homesteading}
+See for example, the Discover television show, ``Alaska the Last Frontier,'' any issue of ``Mother Earth News,'' or Backyard Chicken feeds on Instagram.  
+ 
+ 
+ \bibitem{Haspel}
 In defense of corn, the world’s most important food crop
 The Washington Post
 Tamar Haspel 
 July 12 2015
 
-
-\bibitem{homesteading}
-See for example, the Discover television show, ``Alaska the Last Frontier,'' any issue of ``Mother Earth News,'' or Backyard Chicken feeds on Instagram.  
-
 \bibitem{backyard_homestead}
 The Backyard Homestead: Produce all the food you need on just a quarter acre!
 Carleen Madigan
 Storey Publishing, LLC; 14th Printing edition (February 11, 2009)
 
 
+
 \bibitem{USDA_1917_yields_pamphlet}
 Human Food from an Acre of Staple Farm Products
 Morton O. Cooper and W.J. Spillman
@@ -333,6 +363,8 @@ American Scientist
 vol 63
 413-419
 
+\bibitem{calorie_age} Is $3000\frac{kcal}{person\cdot day}$ accurate for a family?  For soldiers or active athletes it is, but $2000kcal$ is the USDA reference for an ``average adult,'' e.g. the author, in his 40's, and   $1000-1200kcal$ for a senior age ($>60$) female.  However, weeding the garden all day is physically taxing, mice will probably eat some of the potatoes, and $3000$ is a nice round number, so that's what I'm using.
+
 \bibitem{organic_corn_yield}
 This is an old article 
 1998
@@ -352,6 +384,21 @@ ALEJANDRA BORUNDA
 CÉSAR RODRÍGUEZ
 JUNE 30, 2022
 
+\bibitem{HortTech_2019}
+Chinampas: An Urban Farming Model of the Aztecs and a Potential Solution for Modern Megalopolis
+HortTechnology
+Roland Ebel
+Volume/Issue: Volume 30: Issue 1
+2019
+DOI: https://doi.org/10.21273/HORTTECH04310-19
+
+\bibitem{Chinampas_1964}
+THE CHINAMPAS OF MEXICO
+Author(s): Michael D. Coe
+Source: Scientific American , Vol. 211, No. 1 (July 1964), pp. 90-99
+Published by: Scientific American, a division of Nature America, Inc.
+Stable URL: https://www.jstor.org/stable/10.2307/24931564
+
 \bibitem{google_earth}
 Chinampas are still visible in sattelite imagery.  See for example latitide=19.268, longitude -99.087